Monobeam transition section construction



Feb. 2, 1960 H. BARTHELMESS MONOBEAM TRANSITION SECTION CONSTRUCTION 2Sheets-Sheet 1 Filed Oct. 6. 1953 INVENTOR HERMANN BARTHELMESS I Feb. 2,1960 BARTHELMESS 2,923,254

MONOBEAM TRANSITION SECTION CONSTRUCTION Filed Oct. 6, 1953 2Sheets-Sheet 2 i g a a a c E 5 E i I i l w r l 4' 0 '57 INVENTOR HERMANNBARTHELMESS ATTORNEYS United States Patent MONOBEAM TRANSITION SECTIONCONSTRUCTION Hermann Barthelmess, Furstenfeldbruck, Upper Bavaria,Germany, assignor to Alweg-Forschung Gesellschaft mit beschrankterHaftung, Koln, Germany This invention relates to improvements intransportation systems and more particularly to integrated vehicle andtrack structures.

While it is presently contemplated that the systems herein disclosedwill find their primary utility in connection with the so-calledmono-track railway systems as disclosed for example in applicationSerial No; 371,106, filed July 27, 1953, certain aspects ofthese-systems are also applicable to the two-rail railway systems now inwidespread use.

The systems with which the present invention is pri marily concerned arecapable of safe, smooth and economical operation at speeds in excess of200 miles per hour. This type of operation is achieved through theprovision of improved track and train assemblies and also through theunique correlation of these assemblies. Such correlation, which isnotably lacking in prior systems, is particularly necessary in operatingthe train at high speed over curved sections of the track structure.

In accordance with the present invention the track curvature andinclinations are correlated with the train structures in such manner asto permit considerably higher and safer speeds and more comfortablepassenger rides than have been obtainable heretofore. As a result ofthis correlation the train is moved along a path closely approaching theturning path of a vehicle moving in non-solid media.

It is generally recognized that, particularly at higher speeds, curvedsections of track must be banked to avoid the imposition of excessivelateral forces upon the train and track structure. It has further beenrecognized that at the entrance and exit sides of curved track sectionswhich are connected to straight or reversed curved sections, atransition curve must be provided to reduce the lateral forces incidentto turning. Generally such transition curves connect a straight line andthe radius of the final curve. In conventional two-rail railway systemssuch banking is usually eifected in the transition "curve merely byraising one of the two rails above the other.-

Thus, the outer wheels of a train traveling along such a banked curveare suddenly raised, tilting the entire vehicle about an axis defined bythe inner rail thus imposing severe lateral shocks upon passengers andcargo. Such transition curves now in use are generally based on thecubic parabola or closely related curves and have been selectedarbitrarily without consideration of the coopera- "ice passengers aresubjected to sudden and unaccustomed movements.

Because of the linear increase of the transverse inclination which isinevitably produced in transition curves based on the cubic parabola avery high rotary acceleration of the vehicle around the axis of theinner rail is established at the beginning and end of the curves sincetheoretically the rotary speed suddenly increases to its full value atthe entrance side of the curve and remains constant over the full lengthof the transition curve and then suddenly falls to zero. This factorimposes high lateral forces on the equipment, passengers and cargo,causes extreme passenger discomfort, imposes heavy stresses on the trackand vehicle running gearand causes instability at high speeds. Further,insuch prior systems which utilize the inner rail of a curve as therotational axis, the center of gravity of the passengers and cargo aresubjected to a sudden lateral shift as the train enters and leaves thetransition curve. The unpleasant effects of this lateral shift are wellknown to any experienced railroad passenger.

It has been discovered that passenger discomfort may be substantiallyeliminated even at high speeds by developing the transition curve insuch a manner that the entire train is turned about a longitudinal tiltaxis disposed well above the level .of the track. The curve is furtherdeveloped so that the selected longitudinal tilt axis is not shiftedlaterally toward the center of curvature and is guided along a smoothcurve so that the train performs only tilting movements. To accomplishthis,

- the track is shifted outwardly away from the center of the forcesacting on the vehicle and the track structure in such a curve are afunction of the square of the velocity, the high speed travel tends tomagnify disproportionately the defects of previous transition curves.Accordingly, particularly at high speeds, sudden shock loads areimposedon the equipment and cargo and the curvature to the extentdictated by the physical dimensions of the train and the amount of tiltand the desired path of the tilt axis. The tilt axis is guided in spacealong a smooth regular curve. In practice, in the case of a passengertrain, the rotational or tilt axis is preferably disposed in atransverse plane lying slightly above the level of the passengerv seatsand in the case of a cargo train the axis is preferably locatedapproximately at the center of gravity of the cargo. In a train carryingpassengers and cargo at different levels, the location of the axis ofrotation of the train may be determined empirically. 7

Further, the transition curves in accordance with the present inventionare so arranged that all aspects of rotary movement of the train carsabout the preselected axis change in accordance with a smooth curverather than linearly as was common in prior constructions. The train andtrack structure are so correlated that the preselected axis of rotationof the train tangentially follows an ideal transition curve from whichthe actual track transition curve is developed. Broadly the tracktransition curve is developed by initially directing the tracktransition curve away from the center of curvature of the final trackcurve and subsequently swinging the track curve back so that at its exitend it approaches tangentially a vertical projection of the transitioncurve followed by the rotational axis of the train. All of the forcesdeveloped in thetrain and track structure due to.

the passage of the train through such a transition curve are parallel tothe vertical axis of the train.

Accordingly, it is the primary purpose and object of the presentinvention to provide improved train and track structures which areconstructed and correlated to facilitate a change of direction of thepath of movement of the train in a smooth, safe manner at speedsheretofore unattainable. It is a further object of the present inventionto provide novel curved train guiding and supporting structures. It isalso an object of the invention to provide novel correlated train andcurved track structures which eliminate or materially reduce ,the shockforces heretofore .as the train moves over the track structure.

It s also an object of the invention to provide novel tlfilJSlilOl'lcurves for transportation systems.

It is a further object of the invention to provide improved correlatedtrain and curved track structures which 'are effective as the trainpasses'over the track structure to produce a rotary motion in the trainwhich varies in accordance w th a smooth substantially sinusoidal curve.

Further ob ects and advantages will become apparent as the descriptionproceeds in connection with the accompanylng drawings in which:

asses-se Figure I'iS a, perspective view of a train and track systemembodying the novel features of the present inventlon;

Figure 2 is a view of a track structure embodying the transition curveof the present invention with the path of travel of the rotational axisof the vehicle indicated in phantom lines;

Figure 3 is a diagrammatic vertical plan view of the track structureshowing the relation between the curve followed by the axis of thevehicle and the actual track curve;

Figures 4 and 5 illustrategraphically the characteristics of the motionof a vehicle as it passes over curved gack sectlons constructed inaccordance with prior prac- Figure 6 is a graph similar to Figures 4 and5 illustratmg the same factors for the systems of the present invention;and

Figures 7 and 8 are views similar to Figures 2 and 3, respectively, butwith references and coordinates added to-facilitate analysis of thetrack structure.

For purposes of illustration the present invention has been shown andwill be described as a mono-track system in which the track structure isa mono-beam of novel construction since it is in such a system that theunique advantages of the invention are most fully reallzed. However, itis to be understood that the invention in several of its aspects may beutilized to advantage in conjunction with or as a modification ofconventional two-rail railway systems or of prior mono-rail systems.

Referring now more particularly to the drawings and especially toFigures 1 and 2 the principal cooperating components of the railway.system shown are the train,

indicated generally at 20, which may comprise a front .or nose car 22having an operators compartment 24 and any desired number of identicalintermediate cars 26 (one shown) and a rear or tail car 28. The system.alsocomprises a mono-beam track construction indicated generally at 30and supporting pylons 32 which support lthe 1mono-beam at any desiredelevation above ground eve The train unit is constructed with dependingside portions 34 which extend downwardly over the sides of the mono-beam30 to a point adjacent the lower surface thereof. Each of the cars isresiliently supported on chassis or truck structures which are describedin detail in the aforesaid application Serial No. 371,106. The

'chassis structures (not shown) include carrying or loadsupporting-wheels which are adapted to ride on a flat rail 36 at'the topof the mono-beam 30 and guiding and tilt control wheels adapted toresiliently engage rails 38 and 40 disposed on the opposite verticalsides of the mono-beam 30. The car bodies and supporting means are sodisposedwith respect to the mono-beam 30 that 4 the train and trackstructures are such as to minimize the l:veight and strengthrequirements of both train and trac The mono-beam 30 and the supportingpylons 32 are preferably formed of poured concrete which may bereinforced as desired in accordance with conventional practice, and maybe of hollow construction to conserve weight and materials and toprovide a closed internal space for power telephone, telegraph, water,gas and fuel lines.

The top and side rails are'preferably of steel and are preferablysupported on a shock absorbing or damping material such as creosotedwood stripping to provide a yielding rail assembly to prevent the directtransmission of shock loads incident to the normal operation of thevehicle between the concrete beam structure and the train.

of rectangular section and its height (the dimension along its majoraxis 41) is preferably twice its width (the dimension along its lateralaxis 43). However, other forms of beams may be used. For example, thebeam may correspond to the form shown except that it may he providedwith beveled corners to minimize turbulence and eddy loss as the vehiclepasses over the beam at high speed. However, in all cases the beam willhave parallel side faces as shown for supporting the guiding rails '38and and a top surface normal to the side surfaces for supporting theload carrying rails 36.

A curved section of track incorporating the novel transition curve ofthe present invention is illustrated particularly in Figure 2. Theportions of the track there shown include a straight track section 44,the section 46 of the track incorporating the transition curve and themain curve section 48. Beyond the illustrated main track curve section48 the track is provided with a further transition curve sectionidentical to the section 46 which merges into a final straight sectionof the track similar to that shown at 44 or into afurther curve.

The path of movement of the axis of tilt of the train as it passes overthe section of the track shown in Figure 2 is shown in phantom lines. Itwill be seen that this path includes a straight section 50, a transitioncurve section 52 and a main curve section 54 corresponding,respectively, to the track sections 44, 46 and 48. The path comprisingthe sectionsSG, 5-2 and 54 may be referred to for convenience as theideal track curve. It will be seen that this ideal curve is so relatedto the actual track curve so that any point on the ideal curve lieson'an extension of the major axis of the beam.

The track beam is gradually and increasingly inclined along the enteringtransition curve section until it is fully banked for a predeterminedtop speed of the train :around the main curve section where the bank ortilt of the train is uniform and the tilt decreases gradually in theexit transition curve section to zero when the top surface of the beamis horizontal at the end of the transi- 'tion curve or to another tiltas required by the radius and direction of the following main curvewhich may have the same or the opposite direction of curvature as thepreceding curve.

Development of the transition curve depends upon the determination ofthe optimum position of the axis of rotation of the train for averageminimum passenger or load disturbance and the desired rotary speed aboutthis axis at eachpoint in the transition curve. The location of the axisof rotation in freight trains depends solely on mechanicalconsiderations and the optimum result is achieved when the axis ofrotation coincides with the average axial center of gravity of theloaded cars. How- 'ever in'the case ofpassenger train operation thepositioning of the axis of rotation depends on a number of physiologicalfactors which determine passenger comfort. 7 'In general the axis ofturning of the train on the transition; curve will-be -iuthe proximityof the center of gravity of average load. When the axis is so positionedboth the load and the passengers will be subjected substantially only tolifting or lowering movements and sudden lateral shocks which causepassenger discomfort or impose severe stresses on the loads areeliminated.

The rotary speed of the train about the preselected axis of rotationwill depend on the lateral distance of the passengers or the loadfrom'the selected axis and the desired rotary speed will vary inverselywith this distance.

Once the axis of rotation and the desired rotary speed about this axisis determined the banking position of the vehicle at any point on thetransition curve will be established which, in turn, fixes the radius ofcurvature of the ideal transition curve at any point. In this manner thecoordinates of all points on the ideal curve may be determined step bystep and from these coordinates the vertical and horizontal coordinatesof the actual track curve may be finally determined. The length of thetransition curve depends upon the capacity of the cars to resisttorsional loads, the strength of the nose boggies of the train and thedesired comfort of the passengers. In practice the length of the curvescan be determined by mathematical formulae depending upon experimentalconstants developed empirically in accordance with each of thesefactors.

The relation of the ideal curve and the track curve is furtherillustrated diagrammatically in plan in Figure 3. As there shown, thetwo curves are in vertical alignment along the straight portions 44, 50.At the entrance side of the transition section the track curve is swungoutwardly away from the center of curvature with respect to the idealcurve followed by the longitudinal axis of rotation of the train. At theexit side of the transition 16 its turning axis vary in accordancewithsmooth'curves which are sinusoidal in nature. In accordance with thepresent invention it has been discovered that the rate of change of therotary acceleration around the preselected turning axis of the vehicleshould be sinusoidal, the maximum values of the rate of change beingdetermined by physiological conditions. Such a rate of change of rotaryacceleration achieved by the ideal curve of the present invention isshown in section d of Figure 6. The integration of this curve produces asinusoidal variation of the rotary acceleration around the longitudinalaxis of the vehicle as shown in section c and a further integrationresults in a rotary speed about this axis which also varies in a smoothcurve of sinusoidal form as shown in section b. As a result the rotaryangle also changes in a smooth continuously varying curve.

As stated above, after the coordinates of all points on the ideal curveare determined to produce the dynamic conditions illustrated in Figure 6the coordinates of the section the track curve tangentially approachesparallelism with a downward vertical projection of the ideal curve. Thisparallelism continues throughout the main curve section at the end ofwhich the illustrated transition curve or a curve having similarcharacteristics is repeated.

Figures 4, 5 and 6 illustrate graphically the dynamics of the movementof the train along prior transition curves (Figures 4 and 5) and thetransition curve of the present invention (Figure 6). In each of thesegraphs, sections a, b, c and d, respectively, plot the angle ofrotation, the rotary speed about the axis of rotation, the rotaryacceleration around this axis and the rate of change of rotaryacceleration against length and thus show the variation in these factorsover the length of the transition curve.

Figure 4 is applicable to a transition curve now in widespread use intwo-rail systems. It will be seen from part a that the angle of rotationincreases linearly and from sections b, c and d that the rotary speedincreases to its full value instantaneously at the entrance side of thecurves and decreases instantaneously from its full value to zero at theexit side of the curve producing infinitely high positive and negativerotary accelerations and rates of change of rotary acceleration in turnproducing extreme passenger discomfort and imposing severe shock loadson the train and track structure.

Figure 5 graphically illustrates the dynamic conditions occurring as thevehicle passes over transition curves based on the cubic parabola orclosely related curves in limited current use.

It will be seen from a comparison of Figures 4 and 5 that thedeleterious effects of the curve of Figure 4 have to some extent beenmitigated in the curve to which Figure 5 applies. However, it will benoted that the rotary angle still changes approximately linearly andthat the rotary acceleration at the entrance and the exit sides of thecurve is objectionably high and it is apparent from section d of Figure5 that the rotary acceleration varies abruptly in a comparatively shorttime interval.

It will be seen from Figure 6 that in the transition curve according tothe present invention all of the dynamic factors relating to the motionof the vehicle about actual track curve may readily be establishedmathematically on the basis of physical factors such as the size of thecars, etc.

The following example illustrates the development of a section oftransition between a straight track section, that is. a track sectionhaving an infinite radius of curvature and a section having a constantradius of curvature assumed to be 1000 meters. For purposes of analysis,it may be assumed that the length of the transition section is 200meters and the vehicles pass the section at an average velocity ofkilometers per hour. The distance h between the lines 50, 52 and 54 andthe top of the track is assumed to be one meter.

Based on these assumptions and known constants, the angle x-max which isthe angle of tilt of the uniformly curved track section 48 and the angleof tilt of the ad jacent transition track section 46 is determined asfollows:

D I 00 max arc em 93X 1000 are S111 0.15385 8 45 The definitions of theseveral angles, radii, distances, increments and decrements whichdetermine the coordinates of the system illustrated in Figures 7 and 8are as follows:

h=distance of lines 50, 52 and 54 from the top of the track x=variableangle of track tilt (in any point I) x-max=angle of track tilt atjunction with section 48 distance of any point I from the origin lengthof section of transition track R=radius of curvature of the line 52 atany point r=radius of curvature of section 48 AB=increment of angle Bbetween the section 50 and a tangent to the line 52 at a selected pointI d distance between consecutive points I (10 meters) AX AY =incrementsof the rectangular coordinates X Y of the line 52.

E=h. sin x, for any point I AX AY =increments and decrements forarriving at the coordinates X Y of a point on the track section 46 fromthe coordinates X Y of a point I on the line 52.

The system of coordinates shown in Figures 7 and 8 has its origin at thejunction of the straight track section and the transition curve, theabscissa being tangent to the longitudinal axis of the straight tracksection at the origin While the ordinate is normal to the longitudinalaxis of the straight track section.

The formulae for determining the increments and decrements of thecoordinates X and Y of the ideal transi tion line are as follows:

AX =d cos B-AN sin B; AY =d sin B-i-AN cos B The formulae for computingthe coordinates X Y of the top of the actual transition track sectionare as follows:

E=h sin x AX=E sin B X =X +AX AY=E cos B Y =Y +AY The coordinates X andY are orthogonal projections upon the horizontal plane of the line 52.

For clarity an optional point I is shown in Figure 8,

v the figure also indicating the coordinates X Y of the point I on theline 52 as well as the coordinates XgYz of a corresponding point I onthe top surface of the track beam. In practice the transition tracksection is divided into segments. In the example given, twenty segmentsof ten meters each are selected and the coordinates for each a point 50meters from the entrance end of the transition I section, will be 4 22'30 at the midpoint of the transition section, 7 57' 18" at a point 150meters from'the entrance end of the section and the final inclination ofthe beam will be 8 45 00''.

The transition curves discussed above have been developed to produceoptimum results insofar as promoting passenger comfort and minimizingshock loads are concerned. However, it is to be understood that improvedresults may also be obtained with transition curves in which thevariation in dynamic factors departs somewhat from that shown in Figure6.

The invention may be embodied in other specific forms without departingfrom the spirit or essential characteristics thereof. The presentembodiment is therefore to be considered in all respects as illustrativeand not restrictive, the scope of the invention being indicated by theappended claims rather than by the foregoing description, and allchanges which come within the meaning and range of equivalency of theclaims are therefore intended to be embraced therein.

What is claimed and desired to be secured by United States LettersPatent is:

1. In a vehicle track, a transition curve track section for connectingmain track sections, at least one of said main track sections beingcurved on a constant radius, comprising a rigid beam having a toprunning surface and parallel side running surface-s all adapted to beengaged by the wheels of a vehicle, the portion of said transitionsection remote from said curved main track section curving smoothlyoutwardly away from the center of curvature of said curved main tracksection, the portion of said' transition section adjacent said curvedmain track section approaching said curved main track sectiontangentially, and the intermediate portion of said transition sectionbeing smoothly reversed to curve in the same direction as said curvedmain track section, each of said portions merging smoothly into theadjacent portion, and said transition section being graduallyandincreasingly tilted along its length about a line located within saidvehicle a fixed predetermined distance 'above the-top surface ofprojection of-the longitudinal axis of the main track section remotefrom the curved main track section, the opposite end of said line beingcurved on the same radius as said curved main track. section and saidline being smoothly curved along its length toward the center-ofcurvature of said curved main track section, and said line being midwayof extensions of the side surfaces of said track.

2. In a vehicle track, a transition curve track section for connectingmain track sections, at least one of said main track sections beingcurved on a constant radius, comprising a rigid beam having a toprunning surface and parallel side running surfaces all adapted to beengaged by the wheels of a vehicle, the portion of said transitionsection remote from said curved main track section curving smoothlyoutwardly away from the center of curvature'of said curved main tracksection, the portion of said transition section adjacent said curvedmain track section approaching said curved main track sectiontangentially, and the intermediate portion of said transition sectionbeing smoothly reversed to curve in the same direction as said curvedmain track section,

each of said portions merging smoothly into the adjacent portion, andsaid transition section being gradually and increasingly tilted alongits length about a line located within said vehicle a fixedpredetermined distance above the top surface of said track, saiddistance being substantially equal to the distance between said toprunning surface of said track and the center of gravity of the loadcarried by said vehicle, one end of said line being tangent to avertical projection of the longitudinal axis of the main track sectionremote from the curved main track section, the opposite end of said linebeing curved on the same radius as said curved main track section andsaid line being smoothly curved along its length toward the center ofcurvature of said curved main track section, and said line being midwayof extensions of the side surfiacesof said track.

3. In a track for a vehicle having passenger seats, a transition curvetrack section for connecting main track sections, at least one of saidmain track sections being curved on a constant radius, comprising arigid beam having a top running surface and parallel side runningsurfaces all adapted to be engaged by the wheels of a vehicle, theportion of said transition section remote from said curved main tracksection curvingsmoothly outwardly away from the center of curvature ofsaid curved main track section, the portion of said transition sectionadjacent said curved main track section approaching said curved maintrack section tangentially, and the intermediate portion of saidtransition section being smoothly reversed to curve in the samedirectionas said curved main track section, each of said portions mergingsmoothly into the adjacent portion, and said transition section beinggradually and increasingly tilted along its length about a line locatedwithin said vehicle a fixed -predetermined distance above the topsurface of said track, said distance being slightly greater than thedistance between said top running surface of said track and saidpassenger seats, one end of said line being tangent to a verticalprojection of the longitudinal axis of the main track section remotefrom the curved main track section, the opposite end of said line beingcurved on the same radius as said curved main track section and saidline being smoothly curved along its length toward the center ofcurvature of said curved main track section,

and said line being midway of extensions of the side surfaces ofsaidtrack.

4. In a monobeam track, a transition curve track section for connectinga straight track section to a curved track section formed on a constantradius comprising a rigid beam having a top running surface and parallelside running surfaces all adapted to be engaged by the said track, oneendof said line being tangent to a vertical 75 wheels of a'vehicle, theportion of said transition track sectionadjacent said "straighttrack-section curving smoothly outwardly away from the center ofcurvature of said curved track section, the portion of said transitionsection adjacent said curved section approaching said curved sectiontangentially and the intermediate portion of said transition tracksection being smoothly reversed to curve in the same direction as saidcurved section, each of said portions merging smoothly into the adjacentportion and said transition track section being gradually andprogressively tilted along its length about a line located within saidvehicle a fixed predetermined distance above said top running surface ofsaid track, one end of said line being tangent to a vertical projectionof the longitudinal axis of said straight track section, the oppositeend of said line being curved on the References Cited in the file ofthis patent UNITED STATES PATENTS McClure et al Sept. 23, 1919 OTHERREFERENCES Notes On Track, by W. M. Camp,.Auburn Park, Chicago, Ill.,1903.

